A New Exploration Of Miranda's Dynamical History
Abstract
We consider the N-body problem of Uranus with its five main satellites Miranda, Ariel, Umbriel, Titania and Oberon. Previous studies have already treated the problem and explained in details the geophysical observations of the surface structure by the modifications on orbital elements of the satellites. These modifications are consequences of the passage through a mean-motion resonance in the past history of the system. The main responsible is the high inclination of Miranda (4.338°), probably due to a mean-motion resonance 3:1 with Umbriel. We re-analyse the problem with new computing tools and improve some previous results by a new global visualization with chaos and orbital scales maps. This new type of representations allows us to detect numerous secondary resonance zones confirmed by frequency analysis. We already know the important role of the secondary resonances in the problem: they cause the escape from the primary resonance and explain the high value of the current inclination of Miranda. We highlight the frequencies of the secondary resonance arguments and clearly identify the associated libration. These numerical results are validated by an analytical model allowing us to approximate the libration arguments in the primary resonance zones. A commensurability between the libration period and the circulation period of the following primary resonance explains the presence of a secondary resonance zone.
- Publication:
-
AAS/Division for Planetary Sciences Meeting Abstracts #44
- Pub Date:
- October 2012
- Bibcode:
- 2012DPS....4411214N